MinT - Best Known (256−122, 256, s)-Nets in Base 4

Best Known (256−122, 256, s)-Nets in Base 4

(256−122, 256, 130)-Net over F₄ — Constructive and digital

Digital (134, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(256−122, 256, 208)-Net over F₄ — Digital

Digital (134, 256, 208)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−122, 256, 2591)-Net in Base 4 — Upper bound on s

There is no (134, 256, 2592)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13692 990426 363373 447773 477469 303923 710131 797309 482522 755104 986088 218289 415647 135950 952149 881371 641252 437948 863351 171441 439220 120668 198775 581814 475626 638960 > 4²⁵⁶ [i]