MinT - Best Known (38, 38+84, s)-Nets in Base 5

Best Known (38, 38+84, s)-Nets in Base 5

(38, 38+84, 78)-Net over F₅ — Constructive and digital

Digital (38, 122, 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]

(38, 38+84, 412)-Net in Base 5 — Upper bound on s

There is no (38, 122, 413)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 19 870629 611776 960061 927211 561730 316373 671649 922768 854784 450881 385634 411296 546417 692025 > 5¹²² [i]