MinT - Best Known (202−52, 202, s)-Nets in Base 4

Best Known (202−52, 202, s)-Nets in Base 4

(202−52, 202, 531)-Net over F₄ — Constructive and digital

Digital (150, 202, 531)-net over F₄, using

t-expansion [i] based on digital (149, 202, 531)-net over F₄, using
- 11 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 71, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(202−52, 202, 648)-Net in Base 4 — Constructive

(150, 202, 648)-net in base 4, using

4¹ times duplication [i] based on (149, 201, 648)-net in base 4, using
- trace code for nets [i] based on (15, 67, 216)-net in base 64, using
  - 3 times m-reduction [i] based on (15, 70, 216)-net in base 64, using
    - base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(202−52, 202, 1630)-Net over F₄ — Digital

Digital (150, 202, 1630)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−52, 202, 167363)-Net in Base 4 — Upper bound on s

There is no (150, 202, 167364)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 321370 962289 801675 065703 572139 047999 232988 488662 907108 906889 397906 817418 520363 442301 481035 382637 717815 502996 351570 605128 > 4²⁰² [i]