MinT - Best Known (107, 216, s)-Nets in Base 4

Best Known (107, 216, s)-Nets in Base 4

(107, 216, 130)-Net over F₄ — Constructive and digital

Digital (107, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 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, 216, 149)-Net over F₄ — Digital

Digital (107, 216, 149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 216, 1699)-Net in Base 4 — Upper bound on s

There is no (107, 216, 1700)-net in base 4, because

1 times m-reduction [i] would yield (107, 215, 1700)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2790 630701 608322 368908 337368 886022 784307 949149 442481 377457 467545 258652 113032 546272 514482 765883 622682 425800 727293 483093 732465 831328 > 4²¹⁵ [i]