MinT - Best Known (82, 82+36, s)-Nets in Base 4

Best Known (82, 82+36, s)-Nets in Base 4

(82, 82+36, 312)-Net over F₄ — Constructive and digital

Digital (82, 118, 312)-net over F₄, using

4¹ times duplication [i] based on digital (81, 117, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 39, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(82, 82+36, 509)-Net over F₄ — Digital

Digital (82, 118, 509)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+36, 22261)-Net in Base 4 — Upper bound on s

There is no (82, 118, 22262)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110429 602908 427605 859214 847188 911391 869862 225311 611230 975747 968045 673710 > 4¹¹⁸ [i]