MinT - Best Known (71, 71+79, s)-Nets in Base 5

Best Known (71, 71+79, s)-Nets in Base 5

(71, 71+79, 82)-Net over F₅ — Constructive and digital

Digital (71, 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]

(71, 71+79, 132)-Net over F₅ — Digital

Digital (71, 150, 132)-net over F₅, using

t-expansion [i] based on digital (67, 150, 132)-net over F₅, using
- net from sequence [i] based on digital (67, 131)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(71, 71+79, 1773)-Net in Base 5 — Upper bound on s

There is no (71, 150, 1774)-net in base 5, because

1 times m-reduction [i] would yield (71, 149, 1774)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 141 486285 892615 684698 368913 346976 900956 623821 110637 573126 115084 074472 263719 212055 088770 327256 104032 491225 > 5¹⁴⁹ [i]