MinT - Best Known (150−94, 150, s)-Nets in Base 5

Best Known (150−94, 150, s)-Nets in Base 5

(150−94, 150, 82)-Net over F₅ — Constructive and digital

Digital (56, 150, 82)-net over F₅, using

t-expansion [i] based on digital (48, 150, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(150−94, 150, 108)-Net over F₅ — Digital

Digital (56, 150, 108)-net over F₅, using

t-expansion [i] based on digital (55, 150, 108)-net over F₅, using
- net from sequence [i] based on digital (55, 107)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 55 and N(F) ≥ 108, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(150−94, 150, 747)-Net in Base 5 — Upper bound on s

There is no (56, 150, 748)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 742 017248 477718 522921 111036 556136 402345 777916 339850 632791 623412 454445 056619 841447 683548 112813 703651 541041 > 5¹⁵⁰ [i]