MinT - Best Known (85, 123, s)-Nets in Base 4

Best Known (85, 123, s)-Nets in Base 4

(85, 123, 312)-Net over F₄ — Constructive and digital

Digital (85, 123, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 41, 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]

(85, 123, 497)-Net over F₄ — Digital

Digital (85, 123, 497)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 123, 20860)-Net in Base 4 — Upper bound on s

There is no (85, 123, 20861)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 145614 716766 253439 172559 305349 995244 763088 266186 736624 632163 058572 792140 > 4¹²³ [i]