MinT - Best Known (115, 212, s)-Nets in Base 4

Best Known (115, 212, s)-Nets in Base 4

(115, 212, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(115, 212, 200)-Net over F₄ — Digital

Digital (115, 212, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 212, 2729)-Net in Base 4 — Upper bound on s

There is no (115, 212, 2730)-net in base 4, because

1 times m-reduction [i] would yield (115, 211, 2730)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 004391 987109 294643 144724 267092 147276 670647 341594 044967 152562 475960 254796 026572 613110 033744 122696 381220 029182 647606 860056 281336 > 4²¹¹ [i]