MinT - Best Known (123−116, 123, s)-Nets in Base 5

Best Known (123−116, 123, s)-Nets in Base 5

(123−116, 123, 22)-Net over F₅ — Constructive and digital

Digital (7, 123, 22)-net over F₅, using

net from sequence [i] based on digital (7, 21)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(123−116, 123, 39)-Net in Base 5 — Upper bound on s

There is no (7, 123, 40)-net in base 5, because

46 times m-reduction [i] would yield (7, 77, 40)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5⁷⁷, 40, S₅, 2, 70), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 49 630836 753181 660492 284521 524197 771213 948726 654052 734375 / 71 > 5⁷⁷ [i]