MinT - Best Known (186−70, 186, s)-Nets in Base 4

Best Known (186−70, 186, s)-Nets in Base 4

(186−70, 186, 130)-Net over F₄ — Constructive and digital

Digital (116, 186, 130)-net over F₄, using

t-expansion [i] based on digital (105, 186, 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]

(186−70, 186, 337)-Net over F₄ — Digital

Digital (116, 186, 337)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−70, 186, 7310)-Net in Base 4 — Upper bound on s

There is no (116, 186, 7311)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9629 289216 463223 303336 783094 329494 898394 916387 511798 267554 278805 986447 541957 154974 491918 002155 778537 790265 671520 > 4¹⁸⁶ [i]