MinT - Best Known (94, 94+114, s)-Nets in Base 4

Best Known (94, 94+114, s)-Nets in Base 4

(94, 94+114, 104)-Net over F₄ — Constructive and digital

Digital (94, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(94, 94+114, 144)-Net over F₄ — Digital

Digital (94, 208, 144)-net over F₄, using

t-expansion [i] based on digital (91, 208, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(94, 94+114, 1112)-Net in Base 4 — Upper bound on s

There is no (94, 208, 1113)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 176624 588391 912137 214234 662424 227114 111492 113606 970755 389666 834833 299957 916120 366362 146157 102586 029465 666641 468541 127662 639720 > 4²⁰⁸ [i]