MinT - Best Known (200−134, 200, s)-Nets in Base 4

Best Known (200−134, 200, s)-Nets in Base 4

(200−134, 200, 66)-Net over F₄ — Constructive and digital

Digital (66, 200, 66)-net over F₄, using

t-expansion [i] based on digital (49, 200, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(200−134, 200, 99)-Net over F₄ — Digital

Digital (66, 200, 99)-net over F₄, using

t-expansion [i] based on digital (61, 200, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(200−134, 200, 485)-Net in Base 4 — Upper bound on s

There is no (66, 200, 486)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 732078 312090 779061 150318 597566 145385 877277 123257 836909 437165 887939 362740 254590 757967 719178 694122 561072 861134 548823 455790 > 4²⁰⁰ [i]