MinT - Best Known (99−40, 99, s)-Nets in Base 16

Best Known (99−40, 99, s)-Nets in Base 16

(99−40, 99, 532)-Net over F₁₆ — Constructive and digital

Digital (59, 99, 532)-net over F₁₆, using

1 times m-reduction [i] based on digital (59, 100, 532)-net over F₁₆, using
- trace code for nets [i] based on digital (9, 50, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(99−40, 99, 1189)-Net over F₁₆ — Digital

Digital (59, 99, 1189)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−40, 99, 505358)-Net in Base 16 — Upper bound on s

There is no (59, 99, 505359)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 161393 801064 447935 573518 725281 691826 447935 512910 010451 710560 061372 074694 963913 348204 382810 103146 639417 536803 799036 884576 > 16⁹⁹ [i]