MinT - Best Known (139−74, 139, s)-Nets in Base 5

Best Known (139−74, 139, s)-Nets in Base 5

(139−74, 139, 82)-Net over F₅ — Constructive and digital

Digital (65, 139, 82)-net over F₅, using

t-expansion [i] based on digital (48, 139, 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]

(139−74, 139, 120)-Net over F₅ — Digital

Digital (65, 139, 120)-net over F₅, using

t-expansion [i] based on digital (61, 139, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(139−74, 139, 1520)-Net in Base 5 — Upper bound on s

There is no (65, 139, 1521)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 449108 153582 441329 334073 812129 370586 423613 869679 211341 381023 322112 009126 981619 499168 956960 151925 > 5¹³⁹ [i]