MinT - Best Known (75, 75+141, s)-Nets in Base 4

Best Known (75, 75+141, s)-Nets in Base 4

(75, 75+141, 104)-Net over F₄ — Constructive and digital

Digital (75, 216, 104)-net over F₄, using

t-expansion [i] based on digital (73, 216, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(75, 75+141, 112)-Net over F₄ — Digital

Digital (75, 216, 112)-net over F₄, using

t-expansion [i] based on digital (73, 216, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(75, 75+141, 577)-Net in Base 4 — Upper bound on s

There is no (75, 216, 578)-net in base 4, because

1 times m-reduction [i] would yield (75, 215, 578)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2897 747959 271461 408562 458284 954447 190905 801709 094063 042426 011187 000656 662610 659817 653882 617587 673186 795357 169805 278192 231997 315840 > 4²¹⁵ [i]