MinT - Best Known (253−219, 253, s)-Nets in Base 2

Best Known (253−219, 253, s)-Nets in Base 2

(253−219, 253, 24)-Net over F₂ — Constructive and digital

Digital (34, 253, 24)-net over F₂, using

t-expansion [i] based on digital (33, 253, 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]

(253−219, 253, 28)-Net over F₂ — Digital

Digital (34, 253, 28)-net over F₂, using

t-expansion [i] based on digital (33, 253, 28)-net over F₂, using
- net from sequence [i] based on digital (33, 27)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 28, using
    - Drinfeld modules of rank 1 [i]

(253−219, 253, 42)-Net in Base 2 — Upper bound on s

There is no (34, 253, 43)-net in base 2, because

45 times m-reduction [i] would yield (34, 208, 43)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁰⁸, 43, S₂, 5, 174), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 87211 741538 023920 234213 366675 539576 764085 000878 579732 757476 278272 / 175 > 2²⁰⁸ [i]