MinT - Best Known (96, 96+127, s)-Nets in Base 4

Best Known (96, 96+127, s)-Nets in Base 4

(96, 96+127, 104)-Net over F₄ — Constructive and digital

Digital (96, 223, 104)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(96, 96+127, 144)-Net over F₄ — Digital

Digital (96, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 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]

(96, 96+127, 1020)-Net in Base 4 — Upper bound on s

There is no (96, 223, 1021)-net in base 4, because

1 times m-reduction [i] would yield (96, 222, 1021)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 261501 587827 254975 289914 333157 542366 932656 230799 770157 453802 993269 833526 733510 775156 186726 640274 507738 707930 361744 267491 371590 945664 > 4²²² [i]