MinT - Best Known (133, 133+119, s)-Nets in Base 4

Best Known (133, 133+119, s)-Nets in Base 4

(133, 133+119, 130)-Net over F₄ — Constructive and digital

Digital (133, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(133, 133+119, 211)-Net over F₄ — Digital

Digital (133, 252, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+119, 2721)-Net in Base 4 — Upper bound on s

There is no (133, 252, 2722)-net in base 4, because

1 times m-reduction [i] would yield (133, 251, 2722)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 110181 402278 198610 900178 418937 817186 411963 761075 244112 401944 027276 309406 360443 511870 699924 264918 315314 635323 277232 979319 317742 103376 576624 673762 418240 > 4²⁵¹ [i]