MinT - Best Known (124−63, 124, s)-Nets in Base 5

Best Known (124−63, 124, s)-Nets in Base 5

(124−63, 124, 82)-Net over F₅ — Constructive and digital

Digital (61, 124, 82)-net over F₅, using

t-expansion [i] based on digital (48, 124, 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]

(124−63, 124, 120)-Net over F₅ — Digital

Digital (61, 124, 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]

(124−63, 124, 1819)-Net in Base 5 — Upper bound on s

There is no (61, 124, 1820)-net in base 5, because

1 times m-reduction [i] would yield (61, 123, 1820)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 965681 367120 303073 337529 203723 479094 919441 823752 861903 225676 741767 219891 744649 546481 > 5¹²³ [i]