MinT - Best Known (98, 98+145, s)-Nets in Base 4

Best Known (98, 98+145, s)-Nets in Base 4

(98, 98+145, 104)-Net over F₄ — Constructive and digital

Digital (98, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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+145, 144)-Net over F₄ — Digital

Digital (98, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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+145, 914)-Net in Base 4 — Upper bound on s

There is no (98, 243, 915)-net in base 4, because

1 times m-reduction [i] would yield (98, 242, 915)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51 860129 843339 157585 936029 696656 811658 375932 457239 761173 739482 732535 434352 138370 161019 074704 784204 945751 005778 291668 274705 807450 928881 117569 539340 > 4²⁴² [i]