MinT - Best Known (142−95, 142, s)-Nets in Base 5

Best Known (142−95, 142, s)-Nets in Base 5

(142−95, 142, 78)-Net over F₅ — Constructive and digital

Digital (47, 142, 78)-net over F₅, using

t-expansion [i] based on digital (38, 142, 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]

(142−95, 142, 92)-Net over F₅ — Digital

Digital (47, 142, 92)-net over F₅, using

net from sequence [i] based on digital (47, 91)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(142−95, 142, 540)-Net in Base 5 — Upper bound on s

There is no (47, 142, 541)-net in base 5, because

1 times m-reduction [i] would yield (47, 141, 541)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 388 511027 245979 373299 298125 055360 434476 203321 725739 487503 802836 437640 910170 006936 895566 021786 872125 > 5¹⁴¹ [i]