MinT - Best Known (233−208, 233, s)-Nets in Base 2

Best Known (233−208, 233, s)-Nets in Base 2

(233−208, 233, 21)-Net over F₂ — Constructive and digital

Digital (25, 233, 21)-net over F₂, using

t-expansion [i] based on digital (21, 233, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(233−208, 233, 24)-Net over F₂ — Digital

Digital (25, 233, 24)-net over F₂, using

net from sequence [i] based on digital (25, 23)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 25 and N(F) ≥ 24, using
  - Drinfeld modules of rank 1 [i]

(233−208, 233, 32)-Net in Base 2 — Upper bound on s

There is no (25, 233, 33)-net in base 2, because

42 times m-reduction [i] would yield (25, 191, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁹¹, 33, S₂, 6, 166), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 596324 664861 734672 564399 995204 728309 529723 767224 083278 725120 / 167 > 2¹⁹¹ [i]