MinT - Best Known (102, 102+49, s)-Nets in Base 4

Best Known (102, 102+49, s)-Nets in Base 4

(102, 102+49, 240)-Net over F₄ — Constructive and digital

Digital (102, 151, 240)-net over F₄, using

4¹ times duplication [i] based on digital (101, 150, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 50, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(102, 102+49, 480)-Net over F₄ — Digital

Digital (102, 151, 480)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+49, 18909)-Net in Base 4 — Upper bound on s

There is no (102, 151, 18910)-net in base 4, because

1 times m-reduction [i] would yield (102, 150, 18910)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 039574 653994 235078 596971 954340 074245 748460 499069 443138 902813 714970 920239 369042 507258 811239 > 4¹⁵⁰ [i]