MinT - Best Known (29, 29+33, s)-Nets in Base 5

Best Known (29, 29+33, s)-Nets in Base 5

(29, 29+33, 51)-Net over F₅ — Constructive and digital

Digital (29, 62, 51)-net over F₅, using

t-expansion [i] based on digital (22, 62, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(29, 29+33, 59)-Net over F₅ — Digital

Digital (29, 62, 59)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(29, 29+33, 774)-Net in Base 5 — Upper bound on s

There is no (29, 62, 775)-net in base 5, because

1 times m-reduction [i] would yield (29, 61, 775)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 395243 468121 176583 325738 762746 394494 352321 > 5⁶¹ [i]