MinT - Best Known (125−39, 125, s)-Nets in Base 4

Best Known (125−39, 125, s)-Nets in Base 4

(125−39, 125, 240)-Net over F₄ — Constructive and digital

Digital (86, 125, 240)-net over F₄, using

t-expansion [i] based on digital (85, 125, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (85, 126, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 42, 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]

(125−39, 125, 483)-Net over F₄ — Digital

Digital (86, 125, 483)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−39, 125, 22440)-Net in Base 4 — Upper bound on s

There is no (86, 125, 22441)-net in base 4, because

1 times m-reduction [i] would yield (86, 124, 22441)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 452 528365 894215 287975 145235 660562 645114 917180 221924 246334 143981 916897 568272 > 4¹²⁴ [i]