MinT - Best Known (122−83, 122, s)-Nets in Base 5

Best Known (122−83, 122, s)-Nets in Base 5

(122−83, 122, 78)-Net over F₅ — Constructive and digital

Digital (39, 122, 78)-net over F₅, using

t-expansion [i] based on 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]

(122−83, 122, 436)-Net in Base 5 — Upper bound on s

There is no (39, 122, 437)-net in base 5, because

1 times m-reduction [i] would yield (39, 121, 437)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 852228 214554 207633 267740 262883 862260 395590 642279 296580 271093 321979 381123 778807 431605 > 5¹²¹ [i]