MinT - Best Known (102−64, 102, s)-Nets in Base 4

Best Known (102−64, 102, s)-Nets in Base 4

(102−64, 102, 56)-Net over F₄ — Constructive and digital

Digital (38, 102, 56)-net over F₄, using

t-expansion [i] based on digital (33, 102, 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]

(102−64, 102, 66)-Net over F₄ — Digital

Digital (38, 102, 66)-net over F₄, using

t-expansion [i] based on digital (37, 102, 66)-net over F₄, using
- net from sequence [i] based on digital (37, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 37 and N(F) ≥ 66, using
    - Drinfeld modules of rank 1 [i]

(102−64, 102, 328)-Net in Base 4 — Upper bound on s

There is no (38, 102, 329)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 135639 871744 902159 523094 300996 158821 464211 011615 787116 674630 > 4¹⁰² [i]