MinT - Best Known (91, 228, s)-Nets in Base 4

Best Known (91, 228, s)-Nets in Base 4

(91, 228, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(91, 228, 144)-Net over F₄ — Digital

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]

(91, 228, 836)-Net in Base 4 — Upper bound on s

There is no (91, 228, 837)-net in base 4, because

1 times m-reduction [i] would yield (91, 227, 837)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46767 618875 364963 801111 853589 542350 914466 666360 805481 714945 258981 482849 156735 806246 867407 591243 804188 380334 267962 977573 913215 007472 876885 > 4²²⁷ [i]