MinT - Best Known (205−124, 205, s)-Nets in Base 4

Best Known (205−124, 205, s)-Nets in Base 4

(205−124, 205, 104)-Net over F₄ — Constructive and digital

Digital (81, 205, 104)-net over F₄, using

t-expansion [i] based on digital (73, 205, 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]

(205−124, 205, 129)-Net over F₄ — Digital

Digital (81, 205, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(205−124, 205, 730)-Net in Base 4 — Upper bound on s

There is no (81, 205, 731)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2663 944216 056920 083710 700121 471321 903993 185626 665887 686708 365026 173492 833149 753304 082594 492062 180368 556461 613625 545427 437200 > 4²⁰⁵ [i]