MinT - Best Known (99, 99+108, s)-Nets in Base 4

Best Known (99, 99+108, s)-Nets in Base 4

(99, 99+108, 104)-Net over F₄ — Constructive and digital

Digital (99, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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+108, 144)-Net over F₄ — Digital

Digital (99, 207, 144)-net over F₄, using

t-expansion [i] based on digital (91, 207, 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+108, 1376)-Net in Base 4 — Upper bound on s

There is no (99, 207, 1377)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43743 164898 176896 736668 856176 062083 374397 571051 266705 249150 493824 013973 776211 254611 959356 398718 542164 913293 131414 952885 346464 > 4²⁰⁷ [i]