MinT - Best Known (118−72, 118, s)-Nets in Base 5

Best Known (118−72, 118, s)-Nets in Base 5

(118−72, 118, 78)-Net over F₅ — Constructive and digital

Digital (46, 118, 78)-net over F₅, using

t-expansion [i] based on digital (38, 118, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(118−72, 118, 88)-Net over F₅ — Digital

Digital (46, 118, 88)-net over F₅, using

t-expansion [i] based on digital (45, 118, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(118−72, 118, 671)-Net in Base 5 — Upper bound on s

There is no (46, 118, 672)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30599 894941 954944 645443 196982 074535 633264 255534 650721 222269 172171 806546 143557 365761 > 5¹¹⁸ [i]