MinT - Best Known (256−120, 256, s)-Nets in Base 4

Best Known (256−120, 256, s)-Nets in Base 4

(256−120, 256, 130)-Net over F₄ — Constructive and digital

Digital (136, 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]

(256−120, 256, 219)-Net over F₄ — Digital

Digital (136, 256, 219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−120, 256, 2815)-Net in Base 4 — Upper bound on s

There is no (136, 256, 2816)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13682 957058 417219 549438 321003 864091 690421 146858 200011 900446 863519 518011 553666 958301 425989 064794 802699 473532 776427 800930 479186 756326 784351 580292 549847 834345 > 4²⁵⁶ [i]