MinT - Best Known (136, 258, s)-Nets in Base 4

Best Known (136, 258, s)-Nets in Base 4

(136, 258, 130)-Net over F₄ — Constructive and digital

Digital (136, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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, 258, 215)-Net over F₄ — Digital

Digital (136, 258, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 258, 2713)-Net in Base 4 — Upper bound on s

There is no (136, 258, 2714)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 215071 114758 850636 592689 813289 273408 684627 962574 714345 076239 377875 805211 511817 570349 738417 376343 230663 408718 041894 325197 497964 306219 335814 469753 266320 210080 > 4²⁵⁸ [i]