MinT - Best Known (108−73, 108, s)-Nets in Base 4

Best Known (108−73, 108, s)-Nets in Base 4

(108−73, 108, 56)-Net over F₄ — Constructive and digital

Digital (35, 108, 56)-net over F₄, using

t-expansion [i] based on digital (33, 108, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(108−73, 108, 65)-Net over F₄ — Digital

Digital (35, 108, 65)-net over F₄, using

t-expansion [i] based on digital (33, 108, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(108−73, 108, 264)-Net in Base 4 — Upper bound on s

There is no (35, 108, 265)-net in base 4, because

1 times m-reduction [i] would yield (35, 107, 265)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27249 162434 060578 892840 691822 483285 715317 947239 930906 282558 535632 > 4¹⁰⁷ [i]