MinT - Best Known (226−107, 226, s)-Nets in Base 4

Best Known (226−107, 226, s)-Nets in Base 4

(226−107, 226, 130)-Net over F₄ — Constructive and digital

Digital (119, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 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]

(226−107, 226, 190)-Net over F₄ — Digital

Digital (119, 226, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−107, 226, 2425)-Net in Base 4 — Upper bound on s

There is no (119, 226, 2426)-net in base 4, because

1 times m-reduction [i] would yield (119, 225, 2426)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2908 084666 774676 416663 485782 505501 239384 131220 945709 262171 580506 733024 393148 483362 528119 605576 376893 033053 997808 427340 781958 455423 106842 > 4²²⁵ [i]