MinT - Best Known (107, 212, s)-Nets in Base 4

Best Known (107, 212, s)-Nets in Base 4

(107, 212, 130)-Net over F₄ — Constructive and digital

Digital (107, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(107, 212, 156)-Net over F₄ — Digital

Digital (107, 212, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 212, 1827)-Net in Base 4 — Upper bound on s

There is no (107, 212, 1828)-net in base 4, because

1 times m-reduction [i] would yield (107, 211, 1828)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 091918 447652 446794 321824 726458 935260 844472 394992 780038 155731 268088 207239 929100 196373 754862 262199 746109 656223 454350 841286 621760 > 4²¹¹ [i]