MinT - Best Known (75, 75+155, s)-Nets in Base 4

Best Known (75, 75+155, s)-Nets in Base 4

(75, 75+155, 104)-Net over F₄ — Constructive and digital

Digital (75, 230, 104)-net over F₄, using

t-expansion [i] based on digital (73, 230, 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+155, 112)-Net over F₄ — Digital

Digital (75, 230, 112)-net over F₄, using

t-expansion [i] based on digital (73, 230, 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+155, 545)-Net in Base 4 — Upper bound on s

There is no (75, 230, 546)-net in base 4, because

1 times m-reduction [i] would yield (75, 229, 546)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 786734 269105 464464 316875 188120 719515 231839 612467 031755 376363 683819 850831 364691 613245 234496 782368 409529 763776 773021 420215 671402 926365 505088 > 4²²⁹ [i]