MinT - Best Known (228−191, 228, s)-Nets in Base 2

Best Known (228−191, 228, s)-Nets in Base 2

(228−191, 228, 24)-Net over F₂ — Constructive and digital

Digital (37, 228, 24)-net over F₂, using

t-expansion [i] based on digital (33, 228, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(228−191, 228, 30)-Net over F₂ — Digital

Digital (37, 228, 30)-net over F₂, using

t-expansion [i] based on digital (36, 228, 30)-net over F₂, using
- net from sequence [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

(228−191, 228, 45)-Net in Base 2 — Upper bound on s

There is no (37, 228, 46)-net in base 2, because

5 times m-reduction [i] would yield (37, 223, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²²³, 46, S₂, 5, 186), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2695 994666 715063 979466 701508 701963 067363 714442 254057 248110 361024 921600 / 187 > 2²²³ [i]