MinT - Best Known (250−120, 250, s)-Nets in Base 4

Best Known (250−120, 250, s)-Nets in Base 4

(250−120, 250, 130)-Net over F₄ — Constructive and digital

Digital (130, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(250−120, 250, 199)-Net over F₄ — Digital

Digital (130, 250, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−120, 250, 2444)-Net in Base 4 — Upper bound on s

There is no (130, 250, 2445)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 328354 547937 117804 396715 959413 698326 188526 861125 672496 258787 847781 720873 081245 062887 613358 304320 518518 909321 032062 311473 877856 359135 951978 921355 583080 > 4²⁵⁰ [i]