MinT - Best Known (136−97, 136, s)-Nets in Base 5

Best Known (136−97, 136, s)-Nets in Base 5

(136−97, 136, 78)-Net over F₅ — Constructive and digital

Digital (39, 136, 78)-net over F₅, using

t-expansion [i] based on digital (38, 136, 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]

(136−97, 136, 398)-Net in Base 5 — Upper bound on s

There is no (39, 136, 399)-net in base 5, because

1 times m-reduction [i] would yield (39, 135, 399)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 24028 001615 882029 111030 596819 525281 215526 721429 582778 123858 580896 238801 342497 257109 832447 788865 > 5¹³⁵ [i]