MinT - Best Known (75, 75+129, s)-Nets in Base 4

Best Known (75, 75+129, s)-Nets in Base 4

(75, 75+129, 104)-Net over F₄ — Constructive and digital

Digital (75, 204, 104)-net over F₄, using

t-expansion [i] based on digital (73, 204, 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+129, 112)-Net over F₄ — Digital

Digital (75, 204, 112)-net over F₄, using

t-expansion [i] based on digital (73, 204, 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+129, 616)-Net in Base 4 — Upper bound on s

There is no (75, 204, 617)-net in base 4, because

1 times m-reduction [i] would yield (75, 203, 617)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 170 052028 122764 295378 168282 871395 883785 834451 686503 189358 567154 073903 265556 188601 506878 526597 386907 171880 392293 698761 124735 > 4²⁰³ [i]