MinT - Best Known (8−5, 8, s)-Nets in Base 32

Best Known (8−5, 8, s)-Nets in Base 32

(8−5, 8, 496)-Net over F₃₂ — Constructive and digital

Digital (3, 8, 496)-net over F₃₂, using

32¹ times duplication [i] based on digital (2, 7, 496)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁷, 496, F₃₂, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
    - a code by Danev and Olsson [i]

(8−5, 8, 497)-Net over F₃₂ — Digital

Digital (3, 8, 497)-net over F₃₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(32⁸, 497, F₃₂, 2, 5) (dual of [(497, 2), 986, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁸, 994, F₃₂, 5) (dual of [994, 986, 6]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
    - a code by Danev and Olsson [i]

(8−5, 8, 8455)-Net in Base 32 — Upper bound on s

There is no (3, 8, 8456)-net in base 32, because

1 times m-reduction [i] would yield (3, 7, 8456)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 34362 228629 > 32⁷ [i]