MinT - Best Known (98, 98+113, s)-Nets in Base 4

Best Known (98, 98+113, s)-Nets in Base 4

(98, 98+113, 104)-Net over F₄ — Constructive and digital

Digital (98, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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]

(98, 98+113, 144)-Net over F₄ — Digital

Digital (98, 211, 144)-net over F₄, using

t-expansion [i] based on digital (91, 211, 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]

(98, 98+113, 1264)-Net in Base 4 — Upper bound on s

There is no (98, 211, 1265)-net in base 4, because

1 times m-reduction [i] would yield (98, 210, 1265)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 782529 843274 118098 316807 791430 745564 125013 138731 978127 327698 800540 152505 069654 798945 013617 775234 615724 730091 662119 037664 669000 > 4²¹⁰ [i]