MinT - Best Known (228−128, 228, s)-Nets in Base 4

Best Known (228−128, 228, s)-Nets in Base 4

(228−128, 228, 104)-Net over F₄ — Constructive and digital

Digital (100, 228, 104)-net over F₄, using

t-expansion [i] based on digital (73, 228, 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]

(228−128, 228, 144)-Net over F₄ — Digital

Digital (100, 228, 144)-net over F₄, using

t-expansion [i] based on digital (91, 228, 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]

(228−128, 228, 1096)-Net in Base 4 — Upper bound on s

There is no (100, 228, 1097)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195464 523474 317710 353280 187352 237887 173271 486705 619054 967203 182050 894062 567670 133934 967336 714513 463059 340071 793643 758891 098805 913541 387465 > 4²²⁸ [i]