MinT - Best Known (213−95, 213, s)-Nets in Base 4

Best Known (213−95, 213, s)-Nets in Base 4

(213−95, 213, 130)-Net over F₄ — Constructive and digital

Digital (118, 213, 130)-net over F₄, using

t-expansion [i] based on digital (105, 213, 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]

(213−95, 213, 218)-Net over F₄ — Digital

Digital (118, 213, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−95, 213, 3143)-Net in Base 4 — Upper bound on s

There is no (118, 213, 3144)-net in base 4, because

1 times m-reduction [i] would yield (118, 212, 3144)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 860099 729748 088119 644714 425561 548880 278058 638510 661870 138347 936998 056344 436023 296822 777232 938582 647897 637800 013643 411807 280680 > 4²¹² [i]