MinT - Best Known (136, 136+119, s)-Nets in Base 4

Best Known (136, 136+119, s)-Nets in Base 4

(136, 136+119, 130)-Net over F₄ — Constructive and digital

Digital (136, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(136, 136+119, 222)-Net over F₄ — Digital

Digital (136, 255, 222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+119, 2924)-Net in Base 4 — Upper bound on s

There is no (136, 255, 2925)-net in base 4, because

1 times m-reduction [i] would yield (136, 254, 2925)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 850 695694 511875 574557 725625 296546 224568 013209 434653 370597 372893 879268 217580 025635 784812 185306 617494 803929 328800 166165 920763 713111 390381 398698 310669 916080 > 4²⁵⁴ [i]