MinT - Best Known (123−86, 123, s)-Nets in Base 5

Best Known (123−86, 123, s)-Nets in Base 5

(123−86, 123, 72)-Net over F₅ — Constructive and digital

Digital (37, 123, 72)-net over F₅, using

t-expansion [i] based on digital (31, 123, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(123−86, 123, 76)-Net over F₅ — Digital

Digital (37, 123, 76)-net over F₅, using

t-expansion [i] based on digital (34, 123, 76)-net over F₅, using
- net from sequence [i] based on digital (34, 75)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(123−86, 123, 390)-Net in Base 5 — Upper bound on s

There is no (37, 123, 391)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 98 339974 692070 866318 902923 888787 992997 890546 110821 449132 037925 938957 986121 100451 675125 > 5¹²³ [i]