MinT - Best Known (74, 74+156, s)-Nets in Base 4

Best Known (74, 74+156, s)-Nets in Base 4

(74, 74+156, 104)-Net over F₄ — Constructive and digital

Digital (74, 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]

(74, 74+156, 112)-Net over F₄ — Digital

Digital (74, 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]

(74, 74+156, 531)-Net in Base 4 — Upper bound on s

There is no (74, 230, 532)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 274428 042210 242023 054986 578358 671306 641997 909743 407861 479382 410247 233798 522181 652484 526112 742731 408320 881847 927277 011701 394991 266342 945184 > 4²³⁰ [i]