MinT - Best Known (49, 49+59, s)-Nets in Base 3

Best Known (49, 49+59, s)-Nets in Base 3

(49, 49+59, 48)-Net over F₃ — Constructive and digital

Digital (49, 108, 48)-net over F₃, using

t-expansion [i] based on digital (45, 108, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(49, 49+59, 64)-Net over F₃ — Digital

Digital (49, 108, 64)-net over F₃, using

net from sequence [i] based on digital (49, 63)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]

(49, 49+59, 299)-Net in Base 3 — Upper bound on s

There is no (49, 108, 300)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁸, 300, S₃, 59), but
- the linear programming bound shows that MÂ â‰¥ 7 156885 023491 555356 486563 754588 553928 672110 476432 354100 593020 356133 949323 294527 610418 549980 724692 672847 149704 417870 918124 333965 475454 496104 606185 / 1885 631043 371708 591387 274308 463734 923959 817605 012375 783992 452810 608079 732373 132109 648337 103609 > 3¹⁰⁸ [i]