MinT - Best Known (111−45, 111, s)-Nets in Base 16

Best Known (111−45, 111, s)-Nets in Base 16

(111−45, 111, 534)-Net over F₁₆ — Constructive and digital

Digital (66, 111, 534)-net over F₁₆, using

1 times m-reduction [i] based on digital (66, 112, 534)-net over F₁₆, using
- trace code for nets [i] based on digital (10, 56, 267)-net over F₂₅₆, using
  - net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(111−45, 111, 1277)-Net over F₁₆ — Digital

Digital (66, 111, 1277)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−45, 111, 632926)-Net in Base 16 — Upper bound on s

There is no (66, 111, 632927)-net in base 16, because

1 times m-reduction [i] would yield (66, 110, 632927)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 839235 699346 929492 523327 647650 245532 407692 773268 190571 427345 457393 869873 834497 274274 632012 902943 614013 896766 135631 445919 246933 439961 > 16¹¹⁰ [i]