MinT - Best Known (180−84, 180, s)-Nets in Base 3

Best Known (180−84, 180, s)-Nets in Base 3

(180−84, 180, 74)-Net over F₃ — Constructive and digital

Digital (96, 180, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 69, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. digital (27, 111, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(180−84, 180, 111)-Net over F₃ — Digital

Digital (96, 180, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−84, 180, 874)-Net in Base 3 — Upper bound on s

There is no (96, 180, 875)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77 606711 701487 316998 439129 617476 050883 851465 405325 225469 133221 954716 472394 197797 928421 > 3¹⁸⁰ [i]