MinT - Best Known (98, 227, s)-Nets in Base 4

Best Known (98, 227, s)-Nets in Base 4

(98, 227, 104)-Net over F₄ — Constructive and digital

Digital (98, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 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, 227, 144)-Net over F₄ — Digital

Digital (98, 227, 144)-net over F₄, using

t-expansion [i] based on digital (91, 227, 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, 227, 1047)-Net in Base 4 — Upper bound on s

There is no (98, 227, 1048)-net in base 4, because

1 times m-reduction [i] would yield (98, 226, 1048)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11985 167931 126275 221323 337426 913004 919842 476981 688734 478900 109290 327918 284212 205338 947880 947184 693707 996649 540135 711966 473389 336609 827120 > 4²²⁶ [i]