MinT - Best Known (54, 103, s)-Nets in Base 4

Best Known (54, 103, s)-Nets in Base 4

(54, 103, 66)-Net over F₄ — Constructive and digital

Digital (54, 103, 66)-net over F₄, using

t-expansion [i] based on digital (49, 103, 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]

(54, 103, 96)-Net over F₄ — Digital

Digital (54, 103, 96)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 103, 1163)-Net in Base 4 — Upper bound on s

There is no (54, 103, 1164)-net in base 4, because

1 times m-reduction [i] would yield (54, 102, 1164)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25 891710 918048 305406 398236 235332 824178 708185 986854 923080 404264 > 4¹⁰² [i]