MinT - Best Known (121, 212, s)-Nets in Base 4

Best Known (121, 212, s)-Nets in Base 4

(121, 212, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(121, 212, 245)-Net over F₄ — Digital

Digital (121, 212, 245)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 212, 3871)-Net in Base 4 — Upper bound on s

There is no (121, 212, 3872)-net in base 4, because

1 times m-reduction [i] would yield (121, 211, 3872)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 837585 342176 839793 964555 442698 938055 683685 313334 695168 822476 777754 954349 967692 534115 824799 884712 992319 521910 194728 432364 646936 > 4²¹¹ [i]