MinT - Best Known (99, 99+150, s)-Nets in Base 4

Best Known (99, 99+150, s)-Nets in Base 4

(99, 99+150, 104)-Net over F₄ — Constructive and digital

Digital (99, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(99, 99+150, 144)-Net over F₄ — Digital

Digital (99, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(99, 99+150, 895)-Net in Base 4 — Upper bound on s

There is no (99, 249, 896)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 873850 242929 003320 860051 925909 061127 494271 029909 922973 690684 357414 473807 571354 910920 154605 746053 543174 439503 681576 033025 183676 630730 328775 098484 744399 > 4²⁴⁹ [i]